CLOCKS

The hour hand and the minute hand of a clock move in relation to each other
continuously and at any given point of time, they make an angle between 0 0 and 1800 with each
other.
If the time shown by the clock is known, the angle between the hands can be calculated.
Similarly, if the angle between the hands is known, the time shown by the clock can be found
out.
When we say angle between the hands, we normally refer to the acute/obtuse angles (up to 180 0)
between the two hands and not the reflex angle (>1800).
For solving the problems on clocks, the following points will be helpful.
Minute hand covers 3600 in 1 hour, i.e., in 60 mins. Hence MINUTE HAND COVERS 60 0 PER
MINTUE.
Hour hand covers 3600 in 12 hours. Hence HOUR HAND COVERS 300 PER HOUR.
The following additional points also should be remembered in a period of 12 hours, the hands
make an angle of
00 with each other (i.e., they coincide with other) 11 times.
1800 with each other (i.e., they lie on the same straight line) 11 times.
900 or any other angle with each other 22 times.

QUESTIONS

1. Find the number of times the hands of clock are 180 degrees apart in a day?
2. How many degrees will the minute hand move in the same time, in which the hour-hand
move by 200
3. Between 10 clock and 20 clock how many times do both the hands of a clock be at right
angles?
4. Find the number of times the hands of clock are 360 degrees apart in a day
5. How many times do the two hands of a clock form straight lines in a day?
6. When the two hands are at right angles, they are how many minute spaces apart?
7. What is the correct time of the clock if the two hands of a clock shows as 4:25 in the
mirror?
8. What is the mirror image of the clock if the clock shows as 3:20?
9. What is the angle made by the hours hand in 6 hours?
10. If the hours hand make 27° within some specified time then the minutes hand will make
how many degrees in the same time?
11. What is the angle between the two hands of a clock at 3:15?
12. What is the reflex angle between the two hands of a clock at 3:45?
13. At what time between 4 and 5 O’ clock the two hands of a clock coincide?
14. At what time between 4 and 5 O’clock the two hands of a clock be at right angle?
15. What is the correct time of the clock if the two hands of a clock shows as 5:20 in the
mirror?
16. What is the mirror image of the clock if the clock shows as 1:35?
17. What is the angle made by the minutes hand in 44 minutes?
18. What is the angle made by the minutes hand in 48 minutes?
19. What is the angle made by the hours hand in 3 and half an hour?
20. If the hours hand make 29° within some specified time then the minutes hand will make
how many degrees in the same time?
21. How many times do the two hands of a clock coincide in a day?
22. How many times do the two hands of a clock are exactly opposite to each other in a day?
23. How many times do the two hands of a clock form right angles in a day?
24. How many times do the two hands of a clock form straight lines in a day?
25. A clock strikes once at 1 O’clock, twice at 2 O’clock and so on. What is the total number
of striking in a day?
26. What is the angle between the two hands of a clock at 4:20?
27. What is the angle between the two hands of a clock at 6:20?
28. What is the angle between the two hands of a clock at 7:15?
29. What is the reflex angle between the two hands of a clock at 2:35?
30. At what time between 5 and 6 O’clock the two hands of a clock coincide?
31. If a clock takes 22 sec to strike 12, how much time will it take to strike 6?
32. If a clock takes 33 sec to strike 12, how much time will it take to strike 7?
33. At what time between 4 and 5 O’clock the two hands of a clock be in the same straight
line but not together
34. At what time between 5 and 6 O’clock the two hands of a clock be in the same straight
line but not together
35. At what time between 5 and 6 O’clock the two hands of a clock be at right angle?
36. The reflex angle between the hands of a clock at 10.25 is:
37. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through ------
38. At what time between 7 and 8 o'clock will the hands of a clock be in the same straight
line but, not together?
39. At what time between 5.30 and 6 will the hands of a clock be at right angles?
40. The angle between the minute hand and the hour hand of a clock when the time is 4.20,
is:
41. At what angle the hands of a clock are inclined at 15 minutes past 5?
42. At 3:40, the hour hand and the minute hand of a clock form an angle of:
43. In 16 minutes, the minute hand gains over the hour hand by……
44. when the hands are in the opposite directions, they are ------- minute spaces apart
45. A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show
at 10 PM on the same day?
46. How much does a watch lose per day, if its hands coincide every 64 minutes?
47. A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec
fast at 2 p.m. on the following Monday. When was it correct?
48. An accurate clock shows 8 o'clock in the morning. Through how may degrees will the
hour hand rotate when the clock shows 2 o'clock in the afternoon?
49. What is the angle between the two hands of a clock at 6:30?
50. What is the angle between the two hands of a clock at 9:15?